Abstract
AbstractWe provide moment bounds for expressions of the type $$(X^{(1)} \otimes \cdots \otimes X^{(d)})^T A (X^{(1)} \otimes \cdots \otimes X^{(d)})$$
(
X
(
1
)
⊗
⋯
⊗
X
(
d
)
)
T
A
(
X
(
1
)
⊗
⋯
⊗
X
(
d
)
)
where $$\otimes $$
⊗
denotes the Kronecker product and $$X^{(1)}, \ldots , X^{(d)}$$
X
(
1
)
,
…
,
X
(
d
)
are random vectors with independent, mean 0, variance 1, subgaussian entries. The bounds are tight up to constants depending on d for the case of Gaussian random vectors. Our proof also provides a decoupling inequality for expressions of this type. Using these bounds, we obtain new, improved concentration inequalities for expressions of the form $$\Vert B (X^{(1)} \otimes \cdots \otimes X^{(d)})\Vert _2$$
‖
B
(
X
(
1
)
⊗
⋯
⊗
X
(
d
)
)
‖
2
.
Funder
Division of Mathematical Sciences
National Science Foundation
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Computational Mathematics,Radiology, Nuclear Medicine and imaging,Signal Processing,Algebra and Number Theory,Analysis
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献